More info would help. If you are talking coyotes and smaller the 223 is good out to 3-400 yards roughly. Can be shot further, but doesn't have much poop left in it. If you are talking longer shots being the norm a 22-250 or the 243 are a better bet. If you're talking wolf...I'd say the 243 is good...but I'd even go bigger than that for them.
Also another variable is if you're planning on minimizing pelt damage.
Coyotes and fun des mostly. No wolves around here. It would be n further than 400 yards. Reload will be next after I get started.
With that in mind I'd seriously look at the Ruger American with the newer stiffer stock and get it in 22-250. It has a 1-10 twist and would be great with most any bullet you'd ever want to reload in it. The only down fall (albeit a small one) of most 22-250 is that they've been 1-14 twist for ever.
There's also nothing wrong with the 223, but the 22-250 will be flatter out at 400yards edge...it'll be a bit easier dealing with the drop out at that range.